Stochastic wave-function unravelling of the generalized Lindblad equation

TL;DR

This paper develops a non-linear stochastic wave-function approach for simulating non-Markovian quantum dynamics described by the generalized Lindblad equation, demonstrated on a two-level system in a structured environment.

Contribution

It introduces an efficient non-linear form of stochastic Schrödinger equations for non-Markovian systems, enabling practical simulations and comparison with exact solutions.

Findings

The non-linear stochastic equations can be efficiently simulated.

Simulation results agree with the exact generalized master equation.

The method is demonstrated on a two-level system in a structured bath.

Abstract

We investigate generalized non-Markovian stochastic Schroeodinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010)]. We show, that these SSEs can be translated in a non-linear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath and the results of the simulations are compared with the exact solution of the generalized master equation.